Answer
$2$
Work Step by Step
Recall:
$$\log_a{b}=y \longleftrightarrow a^y=b$$
Let $y=\log_8{64}$
Use the definition above to obtain:
\begin{align*}
\log_8{64}&=y\\
8^y&=64\\
8^y&=8^2
\end{align*}
Use the rule $a^m=a^n\longrightarrow m=n$ to obtain:
\begin{align*}
8^y&=8^2\\
y&=2
\end{align*}
Thus, $\log_8{64}=2$.
